DDMoRe Model Repository

Short description:

A pharmacokinetic-pharmacodynamics-viral load (PKPD-VL) model for human immunodeficiency virus type 1 (HIV-1) [use of differential equations]. Original publication assessed the feasibility of the FOCEI method implemented in NONMEM VI and the SAEM algorithm implemented in Monolix version 2.4 to perform parameter estimation for the PKPD-VD model.

Format:	PharmML (0.6)
Related Publication:	The use of the SAEM algorithm in MONOLIX software for estimation of population pharmacokinetic-pharmacodynamic-viral dynamics parameters of maraviroc in asymptomatic HIV subjects. Chan PL, Jacqmin P, Lavielle M, McFadyen L, Weatherley B Journal of pharmacokinetics and pharmacodynamics, 2/2011, Volume 38, Issue 1, pages: 41-61 Affiliation: Global Pharmacometrics, Pfizer Primary Care Business Unit, Sandwich, Kent, UK. phylinda.chan@pfizer.com Abstract: Using simulated viral load data for a given maraviroc monotherapy study design, the feasibility of different algorithms to perform parameter estimation for a pharmacokinetic-pharmacodynamic-viral dynamics (PKPD-VD) model was assessed. The assessed algorithms are the first-order conditional estimation method with interaction (FOCEI) implemented in NONMEM VI and the SAEM algorithm implemented in MONOLIX version 2.4. Simulated data were also used to test if an effect compartment and/or a lag time could be distinguished to describe an observed delay in onset of viral inhibition using SAEM. The preferred model was then used to describe the observed maraviroc monotherapy plasma concentration and viral load data using SAEM. In this last step, three modelling approaches were compared; (i) sequential PKPD-VD with fixed individual Empirical Bayesian Estimates (EBE) for PK, (ii) sequential PKPD-VD with fixed population PK parameters and including concentrations, and (iii) simultaneous PKPD-VD. Using FOCEI, many convergence problems (56%) were experienced with fitting the sequential PKPD-VD model to the simulated data. For the sequential modelling approach, SAEM (with default settings) took less time to generate population and individual estimates including diagnostics than with FOCEI without diagnostics. For the given maraviroc monotherapy sampling design, it was difficult to separate the viral dynamics system delay from a pharmacokinetic distributional delay or delay due to receptor binding and subsequent cellular signalling. The preferred model included a viral load lag time without inter-individual variability. Parameter estimates from the SAEM analysis of observed data were comparable among the three modelling approaches. For the sequential methods, computation time is approximately 25% less when fixing individual EBE of PK parameters with omission of the concentration data compared with fixed population PK parameters and retention of concentration data in the PD-VD estimation step. Computation times were similar for the sequential method with fixed population PK parameters and the simultaneous PKPD-VD modelling approach. The current analysis demonstrated that the SAEM algorithm in MONOLIX is useful for fitting complex mechanistic models requiring multiple differential equations. The SAEM algorithm allowed simultaneous estimation of PKPD and viral dynamics parameters, as well as investigation of different model sub-components during the model building process. This was not possible with the FOCEI method (NONMEM version VI or below). SAEM provides a more feasible alternative to FOCEI when facing lengthy computation times and convergence problems with complex models.
Contributors:	Phylinda Chan

Context of model development:	Clinical end-point;
Long technical model description:	Key model features: 2 compartment disposition pharmacokinetic model; An inhibitory Emax model actin on the infection rate of the virus and target CD4+ cells; An effect compartment describing a delay in the effect on viral load; Viral dynamics model; Differential equations.;
Model compliance with original publication:	Yes;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	The model was used to describe the following in HIV-1 infected asymptomatic patients after initiation of antiretroviral therapy (different doses of maraviroc for 10 days): 1) the time course of plasma maraviroc concentrations; 2) the drug effect of maraviroc; 3) the dynamics and interaction of target CD4+ cells, actively infected CD4+ cells, latently infected CD4+ cells and viruses.;
Modelling task in scope:	estimation;
Nature of research:	Early clinical development (Phases I and II);
Therapeutic/disease area:	Anti-infectives;

Validation Status:	Annotations are correct.
Certification Comment:	This model is not certified.

Model owner: Phylinda Chan
Submitted: Apr 7, 2016 3:11:56 PM
Last Modified: May 25, 2016 9:44:37 AM

Revisions

Version: 8
- Submitted on: May 25, 2016 9:44:37 AM
- Submitted by: Phylinda Chan
- With comment: Updated model annotations.
Version: 6
- Submitted on: Apr 7, 2016 3:11:56 PM
- Submitted by: Phylinda Chan
- With comment: Edited model metadata online.

Independent variable TIME

Structural Model sm

Variable definitions

$CP = \frac{AMT2}{V2}$

$INH = \frac{CP}{(CP + \frac{IC50}{1000})}$

$V = (POVC \times AMT5)$

$\frac{dAMT1}{dTIME} = (- K12 \times AMT1)$

$\frac{dAMT2}{dTIME} = ((((K12 \times AMT1) + (K32 \times AMT3)) - (K23 \times AMT2)) - (K20 \times AMT2))$

$\frac{dAMT3}{dTIME} = ((- K32 \times AMT3) + (K23 \times AMT2))$

$\frac{dAMT4}{dTIME} = ((LAMBDA - (D \times AMT4)) - ((((1 - INH) \times BETA) \times V) \times AMT4))$

$\frac{dAMT5}{dTIME} = ((((((QA \times (1 - INH)) \times BETA) \times V) \times AMT4) - (DA0 \times AMT5)) + (AL \times AMT6))$

$\frac{dAMT6}{dTIME} = (((((((1 - QA) \times (1 - INH)) \times BETA) \times V) \times AMT4) - (DL \times AMT6)) - (AL \times AMT6))$

$IPRE = {\begin{matrix} (log10 ((POVC \times AMT5)) + 3) & if & (AMT5 \neq 0) \\ 0 & otherwise \end{matrix}$

Initial conditions

$AMT1 = 0$

$AMT2 = 0$

$AMT3 = 0$

$AMT4 = 0$

$AMT5 = 0$

$AMT6 = 0$

PK Macros

$iv (cmt = 1, adm = 1, Tlag = ALAG1)$

$iv (cmt = 4, p = F4, adm = 4)$

$iv (cmt = 5, p = F5, adm = 5)$

$iv (cmt = 6, p = F6, adm = 6)$

Variability Model

Level	Type
DV	residualError
ID	parameterVariability

Covariate Model

Continuous covariate KA

Continuous covariate V3

Continuous covariate Q

Continuous covariate V2

Continuous covariate CL

Continuous covariate FLAG

Parameter Model

Parameters

$POP_RR0$ ;

$POP_LAMBDA$ ;

$POP_DA0$ ;

$POP_IC50MVC$ ;

$POP_LAGE$ ;

$PPV_IIV_RR0$ ;

$PPV_IIV_LAMDBA$ ;

$PPV_IIV_DA0$ ;

$PPV_IIV_IC50$ ;

$RUV_PROP_ERR$ ;

$eta_PPV_IIV_RR0 \sim N (0.0, PPV_IIV_RR0)$ — ID

$eta_PPV_IIV_LAMDBA \sim N (0.0, PPV_IIV_LAMDBA)$ — ID

$eta_PPV_IIV_DA0 \sim N (0.0, PPV_IIV_DA0)$ — ID

$eta_PPV_IIV_IC50 \sim N (0.0, PPV_IIV_IC50)$ — ID

$eps_RUV_PROP_ERR \sim N (0.0, RUV_PROP_ERR)$ — DV

$RR0 = (POP_RR0 \times exp (eta_PPV_IIV_RR0))$

$LAMBDA = (POP_LAMBDA \times exp (eta_PPV_IIV_LAMDBA))$

$DA0 = (POP_DA0 \times exp (eta_PPV_IIV_DA0))$

$IC50 = (POP_IC50MVC \times exp (eta_PPV_IIV_IC50))$

$RMIC = ((RR0 - 1) \times IC50)$

$D = 0.006$

$QA = 0.96$

$DL = 0.0132$

$AL = 0.037$

$POVC = 35.4$

$BETA = \frac{((RR0 \times D) \times DA0)}{((POVC \times LAMBDA) \times (QA + \frac{((1 - QA) \times AL)}{(DL + AL)}))}$

$K12 = KA$

$K20 = \frac{CL}{V2}$

$K23 = \frac{Q}{V2}$

$K32 = \frac{Q}{V3}$

$LagE = POP_LAGE$

$ALAG1 = LagE$

$F4 = \frac{\frac{LAMBDA}{D}}{RR0}$

$F5 = {\begin{matrix} 0 & if & (RR0 \leq 1) \\ \frac{((QA + \frac{((1 - QA) \times AL)}{(DL + AL)}) \times (LAMBDA - (D \times F4)))}{DA0} & otherwise \end{matrix}$

$F6 = {\begin{matrix} 0 & if & (RR0 \leq 1) \\ \frac{((1 - QA) \times (LAMBDA - (D \times F4)))}{(DL + AL)} & otherwise \end{matrix}$

$F7 = 0$

Observation Model

Observation IPRE_obs
Continuous / Residual Data

Parameters

$IPRE_obs = (IPRE + eps_RUV_PROP_ERR)$

Estimation Steps

Estimation Step estimStep_1

Estimation parameters

Initial estimates for non-fixed parameters

$POP_RR0 = 5.94$
$POP_LAMBDA = 1.04$
$POP_DA0 = 0.692$
$POP_IC50MVC = 8.66$
$POP_LAGE = 1.13$
$PPV_IIV_RR0 = 0.558$
$PPV_IIV_LAMDBA = 1.277$
$PPV_IIV_DA0 = 0.048$
$PPV_IIV_IC50 = 2.28$
$RUV_PROP_ERR = 0.0445$

Estimation operations

1) Estimate the population parameters

$target = NMTRAN_CODE$
$cov = true$

Algorithm FOCE INTERACTION

Step Dependencies

estimStep_1

DDMODEL00000089: Chan 2010 - HIV PKPD Viral Load Model